Graph-based resampling and gradient feature integrated reference point cloud quality assessment method and system

Abstract

The present invention provides a graph-based resampling and gradient feature integrated reference point cloud quality assessment method and system. The method comprises: using a graph-based key point resampling method to perform key point extraction on an inputted reference point cloud; obtaining local neighborhood groups of the reference point cloud and a distorted point cloud by division by taking a key point as the center, and clustering points in each local area on the basis of Euclidean distances between the key point and other points in a coordinate space; and respectively extracting three-dimensional gradient amplitude features and three-dimensional gradient pattern features of the reference point cloud and the distorted point cloud to obtain an objective quality score of the distorted point cloud. The present invention has a wide range of applications and has high recognition accuracy, sensitivity and robustness.

Description

Reference point cloud quality assessment method and system based on fusion image resampling and gradient features Technical Field

[0001] The present invention relates to the field of image processing, and in particular to a reference point cloud quality assessment method and system integrating image resampling and gradient features. Background Art

[0002] With the continuous advancement of imaging technology, the demand for three-dimensional data in the field of computer vision is increasing. Due to its flexible representation, 3D point clouds have shown broad application prospects in modern communication systems and have become a common 3D data format in immersive media applications. 3D data contains depth information, which provides a more intuitive sense of space and three-dimensionality in visual expression, consistent with the human visual system's perception and understanding of objects during observation.

[0003] However, point clouds are subject to noise and distortion during data processing, which can lead to distortion and reduce the visual quality of displayed content, thus affecting the end-user's satisfaction with the visual experience. Therefore, designing a point cloud quality assessment method that takes into account the special structural characteristics of point clouds and conforms to human visual characteristics is of great application value to the steady development of point cloud data acquisition, processing, and application. Point cloud quality assessment currently has high theoretical research significance and practical application value.

[0004] Summary of the Invention

[0005] The main purpose of the present invention is to overcome the defects in the existing technology and propose a reference point cloud quality assessment method and system that integrates image resampling and gradient features. It effectively describes the gradient direction characteristics and response intensity changes caused by point cloud distortion, conforms to the human eye's subjective perception of distorted point clouds, and has high recognition accuracy, sensitivity and robustness.

[0006] The present invention adopts the following technical solutions:

[0007] On the one hand, a reference point cloud quality assessment method integrating image resampling and gradient features, comprising:

[0008] S101, using a graph-based key point resampling method to extract key points from the input reference point cloud;

[0009] S102, dividing the reference point cloud and the distorted point cloud into local neighborhood groups centered on the key point, and clustering the points in each local area according to the Euclidean distance between the key point and other points in the coordinate space;

[0010] S103, respectively extracting 3D gradient amplitude features and 3D gradient directional pattern features of the reference point cloud and the distorted point cloud in the local area, calculating 3D gradient amplitude similarity between the reference point cloud and the distorted point cloud based on the 3D gradient amplitude features, calculating 3D gradient directional pattern similarity between the reference point cloud and the distorted point cloud based on the 3D gradient directional pattern features, and calculating a joint 3D gradient feature similarity based on the 3D gradient amplitude similarity and the 3D gradient directional pattern similarity;

[0011] S104 , based on the joint 3D gradient feature similarity, weighted pooling is performed using the response intensity value to obtain an objective quality score of the distorted point cloud.

[0012] Preferably, the S101 specifically includes:

[0013] For the input reference point cloud Using high-pass image filtering method Resample and extract key points; specifically use graph transfer operators To describe the relative position relationship between nodes, N represents the dimension of the graph transfer operator A; use the adjacency matrix W i，j and the transfer matrix D -1 W i，j To represent A, that is, A=D -1 W i，j , each linear shift invariant graph filter is a polynomial function of A:

[0014] Where h(A) represents the linear shift invariant image filter; l represents the lth factor of the linear shift invariant image filter, A l represents the lth power of the graph transition operator; h l represents the lth coefficient; L represents the length of the graphic filter; D represents the degree matrix; D -1 represents the inverse matrix of D; I represents the identity matrix; R represents the spatial dimension, indicating that A belongs to the N×N real number space;

[0015] The high-pass filtering of h(A) is implemented using a Hart graph filter as follows:

[0016] Among them, h HH (A) represents a high-pass filter similar to a Hart graph filter; λ = [λ1λ2...λ N ] represents the N eigenvectors of A; V represents the eigenvalue of A; in the vertex domain of the graph, the i-th point The frequency response formula is:

[0017] in, Represents point i Frequency response formula of Indicates the total number of points in the spatial frequency domain; Represents point i adjacent points of ; express and Graph transfer operator between two points.

[0018] Input reference point cloud Extract key points to generate skeleton point cloud

[0019] Preferably, the S102 specifically includes:

[0020] The resampled key point skeleton point cloud Each point in the point cloud is used as a reference point cloud and distorted point cloud The local regional center, for The i-th key point in use and The Euclidean distance corresponding to the geometric part in the clustering of the neighbors of point i is as follows:

[0021] in, Indicates key points The neighborhood group of the reference point cloud with sphere center and θ as radius; Indicates key points is the neighborhood group of the distorted point cloud with the center of the sphere and θ as the radius; The set of all points in the keypoint skeleton representing the reference point cloud; The set of all points in the keypoint skeleton representing the distorted point cloud; represents the square of the 2-norm.

[0022] Preferably, the S103 specifically includes:

[0023] Based on the reference point cloud The three-dimensional gradient amplitude feature m r (x, y, z) and three-dimensional gradient direction map D r (x, y, z), and distorted point cloud The three-dimensional gradient amplitude feature m d (x, y, z) and gradient direction map D d (x, y, z), calculate the three-dimensional gradient magnitude similarity MS(x, y, z) and three-dimensional gradient direction similarity DS(x, y, z) of the reference point cloud and the distorted point cloud. The calculation formula is as follows:

[0024] Among them, T M and T D is a constant used to ensure numerical stability;

[0025] For point P in the local area of ​​the reference point cloud r (x, y, z), three-dimensional gradient amplitude feature m r The (x, y, z) calculation formula is as follows:

[0026] in, They represent the gradient amplitude differences of points in the local neighborhood group of the reference point cloud in the x, y, and z directions respectively; L r (*) indicates the gradient calculation method on the xyz axis of the points in the local neighborhood group of the reference point cloud;

[0027] Introduce three-dimensional gradient direction to describe the change information in point cloud space, with key points As the center of the sphere, θ is the radius to construct a local area. For the point P that falls in the local area r (x, y, z), the formula for calculating the spherical coordinates of the point is as follows:

[0028] Among them, θ r (x, y, z) represents point P r Polar angle of (x, y, z), φ r (x, y, z) represents point P r The azimuth angles (x, y, z) are clustered according to the spherical coordinate values ​​of all points in the local area. The eight directions of the three-dimensional gradient are set. The points in the local area are clustered in the direction closer to the spherical coordinate value. The eight directions of the three-dimensional gradient are calculated based on the polar angle and azimuth angle and are evenly spaced in space. The specific value calculation formula is:

[0029] in Represents the polar angle θ r (x, y, z) direction, Indicates the azimuth angle φ r The direction of (x, y, z), the combination of the two directions constitutes the eight directions of the three-dimensional gradient;

[0030] Three-dimensional gradient direction map D r The (x, y, z) calculation formula is as follows:

[0031] in, Point P r (x, y, z) convolution kernel in eight directions in three dimensions. The direction of the convolution kernel depends on the direction of the three-dimensional gradient in which the point is clustered; Represents the convolution operation;

[0032] For the point P in the local area of ​​the distorted point cloud d (x, y, z), three-dimensional gradient amplitude feature m d The (x, y, z) calculation formula is as follows:

[0033] in, They represent the gradient amplitude differences of points in the local neighborhood group of the distorted point cloud in the x, y, and z directions respectively; L d (*) represents the gradient calculation method on the xyz axis of the points in the local neighborhood group of the distorted point cloud;

[0034] Introduce three-dimensional gradient direction to describe the change information in point cloud space, with key points As the center of the sphere, θ is the radius to construct a local area. For the point P that falls in the local area d (x, y, z), the formula for calculating the spherical coordinates of the point is as follows:

[0035] Among them, θ d (x, y, z) represents point P d Polar angle of (x, y, z), φ d (x, y, z) represents point P d The azimuth angles (x, y, z) are clustered according to the spherical coordinate values ​​of all points in the local area. The eight directions of the three-dimensional gradient are set. The points in the local area are clustered in the direction closer to the spherical coordinate value. The eight directions of the three-dimensional gradient are calculated based on the polar angle and azimuth angle and are evenly spaced in space. The specific value calculation formula is:

[0036] in Represents the polar angle θ d (x, y, z) direction, Indicates the azimuth angle φ d The direction of (x, y, z), the combination of the two directions constitutes the eight directions of the three-dimensional gradient;

[0037] Three-dimensional gradient direction map D dThe (x, y, z) calculation formula is as follows:

[0038] in, Point P d (x, y, z) convolution kernel in eight directions in three dimensions. The direction of the convolution kernel depends on the direction of the three-dimensional gradient in which the point is clustered;

[0039] The joint 3D gradient feature similarity is calculated based on the 3D gradient magnitude similarity and the 3D gradient direction map similarity as follows: PCGS(x,y,z)=[DS(x,y,z)] α [MS(x,y,z)] 1-α

[0040] Here, the parameter α is a positive number used to adjust the relative importance between DS(x, y, z) and MS(x, y, z).

[0041] Preferably, the S104 is as follows: PCGW(x,y,z)=max(I r (x,y,z),I d (x,y,z))

[0042] Among them, I r (x, y, z) is the response intensity value of the point in the local area of ​​the reference point cloud; I d The response intensity value of the point in the local area of ​​the (x, y, z) distorted point cloud; β represents the number of local areas; Ω ​​represents the local range of the reference point cloud and the distorted point cloud, that is, the three-dimensional point xyz falls within this local range; Score represents the objective quality score of the distorted point cloud.

[0043] Preferably, the response intensity value is calculated using a K-nearest neighbor search algorithm.

[0044] On the other hand, a reference point cloud quality assessment system integrating image resampling and gradient features is proposed, comprising:

[0045] A key point extraction module is used to extract key points from the input reference point cloud using a graph-based key point resampling method;

[0046] The local area point clustering module is used to divide the reference point cloud and the distorted point cloud into local neighborhood groups centered on the key points, and cluster the points in each local area according to the Euclidean distance between the key points and other points in the coordinate space;

[0047] a gradient feature similarity calculation module for respectively extracting the 3D gradient amplitude features and 3D gradient directional map features of the reference point cloud and the distorted point cloud in a local area, calculating the 3D gradient amplitude similarity of the reference point cloud and the distorted point cloud based on the 3D gradient amplitude features, calculating the 3D gradient directional map similarity of the reference point cloud and the distorted point cloud based on the 3D gradient directional map features, and calculating the joint 3D gradient feature similarity based on the 3D gradient amplitude similarity and the 3D gradient directional map similarity;

[0048] The quality assessment module is used to obtain the objective quality score of the distorted point cloud based on the joint 3D gradient feature similarity and weighted pooling using the response intensity value.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] (1) The present invention extracts the geometric information of the reference point cloud through a graph-based resampling method to generate a key point skeleton, constructs a local area parameterized model with the key point as the center of the sphere for the reference point cloud and the distorted point cloud, measures the similarity of the gradient amplitude and gradient direction respectively, and finally uses a weighted merging calculation method of the response intensity value to perform weighted pooling on the similarity of these two features to calculate the point cloud quality evaluation score, which effectively describes the gradient direction characteristics and response intensity changes caused by point cloud distortion, conforms to the subjective perception of the human eye for distorted point clouds, has high recognition accuracy, sensitivity and robustness, and has good point cloud quality evaluation performance;

[0051] (2) The present invention extracts the geometric information of the reference point cloud through a graph-based resampling method to generate a key point skeleton, which solves the problem of difficult feature mapping of reference and distorted point clouds in quality assessment. The sampled key points not only conform to human perception but also significantly reduce computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] FIG1 is a flow chart of a method for assessing reference point cloud quality by fusing image resampling and gradient features according to an embodiment of the present invention;

[0053] FIG2 is a structural flow chart of a method for evaluating reference point cloud quality by fusing image resampling and gradient features according to an embodiment of the present invention;

[0054] FIG3 is a structural block diagram of a reference point cloud quality assessment system integrating image resampling and gradient features according to an embodiment of the present invention. DETAILED DESCRIPTION

[0055] Below in conjunction with specific embodiment, further set forth the present invention.Should be understood that these embodiments are only used to illustrate the present invention and are not used in limiting the scope of the present invention.In addition, should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall equally within the scope limited by the appended claims of the application.

[0056] 1 and 2 , a reference point cloud quality assessment method integrating image resampling and gradient features of the present invention comprises the following specific steps:

[0057] S101, using a graph-based key point resampling method to extract key points from the input reference point cloud.

[0058] Specifically, receive the input reference point cloud A high-pass image filtering method is used to Resample to extract key points. Use graph transfer operator To describe the relative position relationship between nodes, N represents the dimension of the graph transfer operator A; A can use the adjacency matrix W i，j and the transfer matrix D -1 W i，j To express, that is, A=D -1 W i，j Each linear shift invariant graph filter is a polynomial function of A:

[0059] Where h(A) represents the linear shift invariant image filter; A l represents the lth power of the graph transition operator; h l represents the lth coefficient; L represents the length of the graphic filter; D represents the degree matrix; D -1 represents the inverse matrix of D; I represents the identity matrix; R represents the spatial dimension, indicating that A belongs to the N×N real number space.

[0060] In this embodiment, a Hart graph filter is used to implement high-pass filtering of h(A):

[0061] Among them, h HH (A) represents a high-pass filter similar to a Hart graph filter; λ = [λ1λ2...λ N ] represents the N eigenvectors of A; V represents the eigenvalue of A; in the vertex domain of the graph, the i-th point The frequency response formula of (a certain point in the spatial frequency domain of the reference point cloud) is:

[0062] in, Represents point i Frequency response formula of Indicates the total number of points in the spatial frequency domain; Represents point i adjacent points of ; express and Graph transfer operator between two points.

[0063] Used to compare the reference point cloud in the spatial frequency domain The sorting is performed for sampling, which reflects how much information about the i-th point can be collected from its neighboring points. The point with more information is more likely to be selected as a keypoint. Finally, the filter length L = 4 and the number of effective keypoints after resampling β = N / 1000 are selected to achieve a balance between complexity and efficiency.

[0064] S102, dividing the reference point cloud and the distorted point cloud into local neighborhood groups with the key point as the center, and clustering the points in each local area according to the Euclidean distance between the key point and other points in the coordinate space.

[0065] Specifically, the resampled key point skeleton point cloud Each point in the point cloud is used as a reference point cloud and distorted point cloud The local regional center, for The i-th key point in This method uses and The Euclidean distance corresponding to the geometric part in the clustering of the neighbors of point i is as follows:

[0066] in, and Representing key points is the neighborhood group of the reference and distorted point clouds with the center of the sphere and θ as the radius; The set of all points in the keypoint skeleton representing the reference point cloud; The set of all points in the keypoint skeleton representing the distorted point cloud; represents the square of the two-norm; the superscript c represents the geometric properties of the point cloud.

[0067] S103, respectively extracting the three-dimensional gradient amplitude features and three-dimensional gradient directional map features of the reference point cloud and the distorted point cloud in the local area, calculating the three-dimensional gradient amplitude similarity of the reference point cloud and the distorted point cloud based on the three-dimensional gradient amplitude features, calculating the three-dimensional gradient directional map similarity of the reference point cloud and the distorted point cloud based on the three-dimensional gradient directional map features, and calculating the joint three-dimensional gradient feature similarity based on the three-dimensional gradient amplitude similarity and the three-dimensional gradient directional map similarity.

[0068] Specifically, based on the extraction of 3D gradient amplitude features, the calculation method of 3D gradient in eight directions is expanded, the K-nearest neighbor search algorithm is used to calculate the response intensity value of each point, and a local parameterized model of 3D gradient information is constructed as follows.

[0069] For a point P(x, y, z) in a local area of ​​a 3D point cloud, the 3D gradient amplitude calculation formula is as follows: x =L(x+1,y,z)-L(x-1,y,z) L y =L(x,y+1,z)-L(x,y-1,z) L z =L(x,y,z+1)-L(x,y,z-1)

[0070] Among them, L x , L y , L z It represents the gradient magnitude difference of the points in each local neighborhood group in three directions.

[0071] The division angle formula of the eight directions of the three-dimensional gradient is as follows:

[0072] The calculation formula of its gradient directional map is as follows:

[0073] Among them, L Dir for the reason 三 The convolution kernel in the direction of point P (x, y, z) calculated by the eight-dimensional gradient division angle; Represents the convolution operation.

[0074] A local parameterized model is used to extract the 3D gradient features of the reference and distorted point clouds and calculate their feature similarity, including 3D gradient amplitude features and gradient direction map features.

[0075] Specifically, according to the reference point cloud The three-dimensional gradient amplitude feature m r (x, y, z) and gradient direction map D r (x, y, z), and distorted point cloud The three-dimensional gradient amplitude feature m d (x, y, z) and gradient direction map D d (x, y, z), calculate the three-dimensional gradient magnitude similarity MS(x, y, z) and three-dimensional gradient direction similarity DS(x, y, z) of the reference point cloud and the distorted point cloud. The calculation formula is as follows:

[0076] Among them, T M and T D is a constant used to ensure numerical stability.

[0077] This embodiment combines the three-dimensional gradient amplitude and the directional similarity as comprehensive indicators for point cloud quality assessment. The calculation method can be expressed as their combination: PCGS(x,y,z)=[DS(x,y,z)] α [MS(x,y,z)] 1-α

[0078] Here, the parameter α is a positive number used to adjust the relative importance between DS(x, y, z) and MS(x, y, z).

[0079] S104 , based on the joint 3D gradient feature similarity, weighted pooling is performed using the response intensity value to obtain an objective quality score of the distorted point cloud.

[0080] Specifically, the point cloud objective quality score Score is calculated using the three-dimensional response intensity value weighted pooling method as follows: PCGW(x,y,z)=max(I r (x,y,z),I d (x,y,z))

[0081] Among them, I r (x, y, z) and I d (x, y, z) is the reference point 云 and distortion point 云 The larger value of the response intensity value is selected as the weight PCGW in the three-dimensional edge strength pooling strategy; Ω represents the local range of the reference point cloud and the distorted point cloud, that is, the three-dimensional point xyz falls within this local range; Score represents the objective quality score of the distorted point cloud.

[0082] As shown in FIG3 , a reference point cloud quality assessment system integrating image resampling and gradient features includes:

[0083] A key point extraction module 301 is used to extract key points from an input reference point cloud using a graph-based key point resampling method;

[0084] A local area point clustering module 302 is used to divide the reference point cloud and the distorted point cloud into local neighborhood groups centered on the key point, and cluster the points in each local area according to the Euclidean distance between the key point and other points in the coordinate space;

[0085] a gradient feature similarity calculation module 303 for respectively extracting 3D gradient amplitude features and 3D gradient directional pattern features of the reference point cloud and the distorted point cloud within a local area, calculating 3D gradient amplitude similarity between the reference point cloud and the distorted point cloud based on the 3D gradient amplitude features, calculating 3D gradient directional pattern similarity between the reference point cloud and the distorted point cloud based on the 3D gradient directional pattern features, and calculating a joint 3D gradient feature similarity based on the 3D gradient amplitude similarity and the 3D gradient directional pattern similarity;

[0086] The quality assessment module 304 is configured to perform weighted pooling using the response intensity value based on the joint three-dimensional gradient feature similarity to obtain an objective quality score of the distorted point cloud.

[0087] This embodiment is a specific implementation of a reference point cloud quality assessment system that integrates image resampling and gradient features. The above-mentioned reference point cloud quality assessment method that integrates image resampling and gradient features will not be repeated in this embodiment.

[0088] The above is only a specific implementation of the present invention, but the design concept of the present invention is not limited to this. Any non-substantial changes to the present invention using this concept shall be deemed as an infringement of the protection scope of the present invention. Industrial Applicability

[0089] The present invention provides a reference point cloud quality assessment method and system that integrates graph resampling and gradient features. The method uses a graph-based key point resampling method to extract key points from an input reference point cloud. The method divides the reference point cloud and the distorted point cloud into local neighborhood groups centered on the key points, and clusters the points in each local area according to the Euclidean distance between the key points and other points in the coordinate space. The method also extracts the three-dimensional gradient amplitude features and three-dimensional gradient direction map features of the reference point cloud and the distorted point cloud, respectively, to obtain an objective quality score for the distorted point cloud. The method has a wide range of applications and has high recognition accuracy, sensitivity, and robustness.

Claims

1. A reference point cloud quality assessment method integrating image resampling and gradient features, characterized in that: include: S101, extracting key points from the input reference point cloud using a graph-based key point resampling method; S102, dividing the reference point cloud and the distorted point cloud into local neighborhood groups with the key point as the center, and clustering the points in each local area according to the Euclidean distance between the key point and other points in the coordinate space; S103, respectively extracting 3D gradient amplitude features and 3D gradient directional map features of the reference point cloud and the distorted point cloud in the local area, calculating the 3D gradient amplitude similarity of the reference point cloud and the distorted point cloud based on the 3D gradient amplitude features, calculating the 3D gradient directional map similarity of the reference point cloud and the distorted point cloud based on the 3D gradient directional map features, and calculating the joint 3D gradient feature similarity based on the 3D gradient amplitude similarity and the 3D gradient directional map similarity; S104, based on the joint three-dimensional gradient feature similarity, weighted pooling is performed using the response intensity value to obtain an objective quality score of the distorted point cloud; The S101 specifically includes: For the input reference point cloud Using high-pass image filtering Resample and extract key points; specifically use the graph transfer operator A∈R N×N To describe the relative position relationship between nodes, N represents the dimension of the graph transfer operator A; use the adjacency matrix W i,j With the transfer matrix D -1 W i,j To represent A, that is, A=D -1 W i,j , each linear shift invariant graph filter is a polynomial function of A: Where h(A) represents the linear shift invariant image filter; l represents the lth factor of the linear shift invariant image filter, A l represents the lth power of the graph transition operator; h l represents the lth coefficient; L represents the length of the graphic filter; D represents the degree matrix; D -1 represents the inverse matrix of D; I represents the identity matrix; R represents the spatial dimension, indicating that A belongs to the N×N real number space; Input reference point cloud Extract key points to generate skeleton point cloud The S103 specifically includes: Based on the reference point cloud The three-dimensional gradient amplitude feature m r (x, y, z) and three-dimensional gradient direction map D r (x,y,z), and distorted point cloud The three-dimensional gradient amplitude feature m d (x,y,z) and gradient direction map D d (x, y, z), calculate the three-dimensional gradient amplitude similarity MS(x, y, z) and three-dimensional gradient direction similarity DS(x, y, z) of the reference point cloud and the distorted point cloud, the calculation formula is as follows: Among them, T M and T D is a constant used to ensure numerical stability; For point P in the local area of ​​the reference point cloud r (x,y,z), three-dimensional gradient amplitude feature m r The calculation formula for (x,y,z) is as follows: in, They represent the gradient amplitude differences of points in the local neighborhood group of the reference point cloud in the x, y, and z directions respectively; L r (*) indicates the gradient calculation method on the xyz axis of the points in the local neighborhood group of the reference point cloud.

2. The reference point cloud quality assessment method of fusion image resampling and gradient features according to claim 1, characterized in that: In S101, a Hart-like filter is used to implement high-pass filtering of h(A) as follows: Among them, h HH (A) represents a high-pass filter similar to a Hart graph filter; λ = [λ1 λ2 ... λ N ] represents the N eigenvectors of A; V represents the eigenvalue of A; in the vertex domain of the graph, the i-th point The frequency response formula is: in, Represents the i-th point The frequency response formula of ; N represents the total number of points in the spatial frequency domain; Represents the i-th point The adjacent points of express and Graph transfer operator between two points.

3. The reference point cloud quality assessment method of fusion image resampling and gradient features according to claim 1 or 2, characterized in that: The S102 specifically includes: The resampled key point skeleton point cloud Each point in the point cloud is used as a reference and distorted point cloud The local regional center, for The i-th key point in use and The Euclidean distance corresponding to the geometric part in the clustering of the neighbors of point i is as follows: in, Indicates key points is the neighborhood group of the reference point cloud with the center of the sphere and θ as the radius; Indicates key points is the neighborhood group of the distorted point cloud with the center of the sphere and θ as the radius; The set of all points in the keypoint skeleton representing the reference point cloud; The set of all points in the keypoint skeleton representing the distorted point cloud; represents the square of the second norm; the superscript c represents the geometric properties of the point cloud.

4. The reference point cloud quality assessment method of fusion image resampling and gradient features according to claim 3, characterized in that: The S103 further comprises: The three-dimensional gradient direction is introduced to describe the change information in the point cloud space. is the center of the sphere, θ is the radius to construct a local region. For the point P that falls in the local region r (x,y,z), the formula for calculating the spherical coordinates of the point is as follows: Among them, θ r (x,y,z) represents point P r The polar angle of (x,y,z), φ r (x,y,z) represents point P r The azimuth of (x, y, z) is clustered according to the spherical coordinate values ​​of all points in the local area; the eight directions of the three-dimensional gradient are set, The closer the spherical coordinate value of the points in the local area is to a certain direction, the clustering will be in that direction; the eight directions of the three-dimensional gradient are calculated based on the polar angle and azimuth angle, and are distributed equally in space; the calculation formula for the specific value is: in Represents the polar angle θ r The direction of (x,y,z), Indicates the azimuth angle φ r The direction of (x, y, z), the combination of the two directions constitutes the eight directions of the three-dimensional gradient; Three-dimensional gradient direction map D r The calculation formula for (x,y,z) is as follows: in, Point P r (x, y, z) is the convolution kernel in eight directions in three dimensions. The direction of the convolution kernel depends on the direction of the three-dimensional gradient in which the point is clustered; Represents the convolution operation; For point P in the local area of ​​the distorted point cloud d (x,y,z), three-dimensional gradient amplitude feature m d The calculation formula for (x,y,z) is as follows: in, They represent the gradient amplitude differences of points in the local neighborhood group of the distorted point cloud in the x, y, and z directions respectively; L d (*) represents the gradient calculation method on the xyz axis of the points in the local neighborhood group of the distorted point cloud; The three-dimensional gradient direction is introduced to describe the change information in the point cloud space. is the center of the sphere, θ is the radius to construct a local region. For the point P that falls in the local region d (x,y,z), the formula for calculating the spherical coordinates of the point is as follows: Among them, θ d (x,y,z) represents point P d The polar angle of (x,y,z), φ d (x,y,z) represents point P d The azimuth of (x, y, z) is clustered according to the spherical coordinate values ​​of all points in the local area; the eight directions of the three-dimensional gradient are set, and the points in the local area are clustered in the direction closer to the spherical coordinate value; the eight directions of the three-dimensional gradient are calculated based on the polar angle and azimuth, and are distributed equally in space; the calculation formula for the specific value is: in Represents the polar angle θ d The direction of (x,y,z), Indicates the azimuth angle φ d The direction of (x, y, z), the combination of the two directions constitutes the eight directions of the three-dimensional gradient; Three-dimensional gradient direction map D d The calculation formula for (x,y,z) is as follows: in, For point P d (x, y, z) is the convolution kernel in eight directions in three dimensions. The direction of the convolution kernel depends on the direction of the three-dimensional gradient in which the point is clustered; The joint 3D gradient feature similarity is calculated based on the 3D gradient amplitude similarity and the 3D gradient direction map similarity, as follows: PCGS(x,y,z)=[DS(x,y,z)] α ·[MS(x,y,z)] 1-α Here, the parameter α is a positive number used to adjust the relative importance between DS(x,y,z) and MS(x,y,z).

5. The reference point cloud quality assessment method of fusion image resampling and gradient features according to claim 4, characterized in that: The S104 is specifically as follows: PCGW(x,y,z)=max(I r (x,y,z),I d (x,y,z) Among them, I r (x, y, z) is the response intensity value of the point in the local area of ​​the reference point cloud; I d (x, y, z) is the response intensity value of the point in the local area of ​​the distorted point cloud; β represents the number of local areas; Ω ​​represents the local range of the reference point cloud and the distorted point cloud, that is, the three-dimensional point xyz falls within the local range; Score represents the distorted point Objective quality score of the cloud.

6. The reference point cloud quality assessment method of fusion image resampling and gradient features according to claim 5, characterized in that: The response intensity value is calculated using the K nearest neighbor search algorithm.

7. A reference point cloud quality assessment system integrating image resampling and gradient features, characterized in that: include: A key point extraction module is used to extract key points from the input reference point cloud using a graph-based key point resampling method; The local area point clustering module is used to divide the local neighborhood groups of the reference point cloud and the distorted point cloud with the key point as the center, and cluster the points in each local area according to the Euclidean distance between the key point and other points in the coordinate space; A gradient feature similarity calculation module is used to extract the 3D gradient amplitude feature and the 3D gradient directional map feature of the reference point cloud and the distorted point cloud in the local area respectively, calculate the 3D gradient amplitude similarity of the reference point cloud and the distorted point cloud based on the 3D gradient amplitude feature, calculate the 3D gradient directional map similarity of the reference point cloud and the distorted point cloud based on the 3D gradient directional map feature, and calculate the joint 3D gradient feature similarity based on the 3D gradient amplitude similarity and the 3D gradient directional map similarity; The quality assessment module is used to obtain the objective quality score of the distorted point cloud based on the joint 3D gradient feature similarity and weighted pooling using the response intensity value; The key point extraction module is specifically used for: For the input reference point cloud Using high-pass image filtering Resample and extract key points; Specifically use the graph transfer operator A∈R N×N To describe the relative position relationship between nodes, N represents the dimension of the graph transfer operator A; use the adjacency matrix W i,j With the transfer matrix D -1 W i,j To represent A, that is, A=D -1 W i,j , each linear shift invariant graph filter is a polynomial function of A: Where h(A) represents the linear shift invariant image filter; l represents the lth factor of the linear shift invariant image filter, A l represents the lth power of the graph transition operator; h l represents the lth coefficient; L represents the length of the graphic filter; D represents the degree matrix; D -1 represents the inverse matrix of D; I represents the identity matrix; Input reference point cloud Extract key points to generate skeleton point cloud The gradient feature similarity calculation module is specifically used for: Based on the reference point cloud The three-dimensional gradient amplitude feature m r (x, y, z) and three-dimensional gradient direction map D r (x,y,z), and distorted point cloud The three-dimensional gradient amplitude feature m d (x,y,z) and gradient direction map D d (x, y, z), calculate the three-dimensional gradient amplitude similarity MS(x, y, z) and three-dimensional gradient direction similarity DS(x, y, z) of the reference point cloud and the distorted point cloud, the calculation formula is as follows: Among them, T M and T D is a constant used to ensure numerical stability; For point P in the local area of ​​the reference point cloud r (x,y,z), three-dimensional gradient amplitude feature m r The calculation formula for (x,y,z) is as follows: in, They represent the gradient amplitude differences of points in the local neighborhood group of the reference point cloud in the x, y, and z directions respectively; L r (*) indicates the gradient calculation method on the xyz axis of the points in the local neighborhood group of the reference point cloud.

8. The reference point cloud quality assessment system integrating image resampling and gradient features according to claim 7, characterized in that: The key point extraction module further uses a Hart graph filter to implement high-pass filtering of h(A) as follows: Among them, h HH (A) represents a high-pass filter similar to a Hart graph filter; λ = [λ1 λ2 ... λ N ] represents the N eigenvectors of A; V represents the eigenvalue of A; in the vertex domain of the graph, the i-th point The frequency response formula is: in, Represents the i-th point The frequency response formula of ; N represents the total number of points in the spatial frequency domain; Represents the i-th point adjacent points.

9. The reference point cloud quality assessment system integrating image resampling and gradient features according to claim 7 or 8, characterized in that: The gradient feature similarity calculation module is further used to: The three-dimensional gradient direction is introduced to describe the change information in the point cloud space. is the center of the sphere, θ is the radius to construct a local region. For the point P that falls in the local region r (x,y,z), the formula for calculating the spherical coordinates of the point is as follows: Among them, θ r (x,y,z) represents point P r The polar angle of (x,y,z), φ r (x,y,z) represents point P r The azimuth of (x, y, z) is clustered according to the spherical coordinate values ​​of all points in the local area; the eight directions of the three-dimensional gradient are set, and the points in the local area are clustered in the direction closer to the spherical coordinate value; the eight directions of the three-dimensional gradient are calculated based on the polar angle and azimuth, and are distributed equally in space; the calculation formula for the specific value is: in Represents the polar angle θ r The direction of (x,y,z), Indicates the azimuth angle φ r The direction of (x, y, z), the combination of the two directions constitutes the eight directions of the three-dimensional gradient; Three-dimensional gradient direction map D r The calculation formula for (x,y,z) is as follows: in, Point P r (x, y, z) is the convolution kernel in eight directions in three dimensions. The direction of the convolution kernel depends on the direction of the three-dimensional gradient in which the point is clustered; Represents the convolution operation; For the point P in the local area of ​​the distorted point cloud d (x,y,z), three-dimensional gradient amplitude feature m d The calculation formula for (x,y,z) is as follows: in, They represent the gradient amplitude differences of points in the local neighborhood group of the distorted point cloud in the x, y, and z directions respectively; L d (*) represents the gradient calculation method on the xyz axis of the points in the local neighborhood group of the distorted point cloud; The three-dimensional gradient direction is introduced to describe the change information in the point cloud space. is the center of the sphere, θ is the radius to construct a local region. For the point P that falls in the local region d (x,y,z), the formula for calculating the spherical coordinates of the point is as follows: Among them, θ d (x,y,z) represents point P d The polar angle of (x,y,z), φ d (x,y,z) represents point P d The azimuth of (x, y, z) is clustered according to the spherical coordinate values ​​of all points in the local area; the eight directions of the three-dimensional gradient are set, and the points in the local area are clustered in the direction closer to the spherical coordinate value; the eight directions of the three-dimensional gradient are calculated based on the polar angle and azimuth, and are distributed equally in space; the calculation formula for the specific value is: in Represents the polar angle θ d The direction of (x,y,z), Indicates the azimuth angle φ d The direction of (x, y, z), the combination of the two directions constitutes the eight directions of the three-dimensional gradient; Three-dimensional gradient direction map D d The calculation formula for (x,y,z) is as follows: in, For point P d (x, y, z) is the convolution kernel in eight directions in three dimensions. The direction of the convolution kernel depends on the direction of the three-dimensional gradient in which the point is clustered; The joint 3D gradient feature similarity is calculated based on the 3D gradient amplitude similarity and the 3D gradient direction map similarity, as follows: PCGS(x,y,z)=[DS(x,y,z)] α ·[MS(x,y,z)] 1-α Here, the parameter α is a positive number used to adjust the relative importance between DS(x,y,z) and MS(x,y,z).

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